Tropical M\"obius strips and ruled surfaces

Author:

Thomas Blomme, Victoria Schleis

Keyword:

Mathematics, Algebraic Geometry, Algebraic Geometry (math.AG), Combinatorics (math.CO)

journal:

date:

2023-09-12 16:00:00

Abstract

We consider the enumeration of tropical curves in M\"obius strips for two different lattice structures and relate them to the enumeration of curves in two rational ruled surfaces over a complex elliptic curve. Using this correspondence, we prove regularity results such as the piecewise quasi-polynomiality of relative invariants and the quasi-modularity of their generating series.

PDF: Tropical M\"obius strips and ruled surfaces.pdf